My ideal friend is nothing like you posted. I don't compete to be better than my friends. I don't get jealous of my friends. To me, a good friend is somebody that becomes an extension of myself. That is, we are so comfortable with each other that we can talk when we want to, we can hang out silently together too. We can go places or stay home. It's all okay. We can listen to problems and talk about good stuff. But we SUPPORT and don't COMPETE (at least not in a way that we would stress about it... maybe joking competition or something). So yeah, if you think friendship is about you being hotter, smarter, and having a sweeter smile so that you are BETTER than your friends, I can see that you would have a problem finding real friends. But, it sounds like you don't really need any friends either, afterall, who could ever add up to what you already have in yourself?
Sorry to be so straightforward, but it sounds like you have a "poor little perfect me" thing going on...